Atomistic simulation of quantum transport in nanoelectronic devices:
"Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic dev...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2016]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic device simulations. Nevertheless those packages are either black boxes (commercial codes) or accessible only to very limited users (private research codes). The purpose of this book is to open one of the commercial black boxes, and to demonstrate the complete procedure from theoretical derivation, to numerical implementation, all the way to device simulation. Meanwhile the affiliated source code constitutes an open platform for new researchers. This is the first book of its kind. We hope the book will make a modest contribution to the field of computational nanoelectronics"-- |
| Beschreibung: | xxii, 413 Seiten Illustrationen, Diagramme CD-ROM (12 cm) |
| ISBN: | 9789813141421 9813141425 9789813141414 9813141417 |
Internformat
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| 100 | 1 | |a Zhu, Yu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Atomistic simulation of quantum transport in nanoelectronic devices |c Yu Zhu and Lei Liu, NanoAcademic Technologies Inc., Canada |
| 264 | 1 | |a New Jersey |b World Scientific |c [2016] | |
| 300 | |a xxii, 413 Seiten |b Illustrationen, Diagramme |e CD-ROM (12 cm) | ||
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| 520 | |a "Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic device simulations. Nevertheless those packages are either black boxes (commercial codes) or accessible only to very limited users (private research codes). The purpose of this book is to open one of the commercial black boxes, and to demonstrate the complete procedure from theoretical derivation, to numerical implementation, all the way to device simulation. Meanwhile the affiliated source code constitutes an open platform for new researchers. This is the first book of its kind. We hope the book will make a modest contribution to the field of computational nanoelectronics"-- | ||
| 650 | 4 | |a Nanoelectronics / Computer simulation | |
| 650 | 4 | |a Nanoelectromechanical systems | |
| 650 | 4 | |a Transport theory / Data processing | |
| 650 | 4 | |a Electron transport | |
| 650 | 4 | |a Quantum electronics / Mathematical models | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 0 | 7 | |a Computersimulation |0 (DE-588)4148259-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804176437594292224 |
|---|---|
| adam_text | Contents
R
Foreword vii
Preface ix
Acknowledgments xiii
1. Introduction 1
1.1 What is quantum transport?............................ 1
1.2 Every atom counts..................................... 8
1.3 Disorder and coherent potential...................... 13
1.4 NECPA-DFT theory and NanoDsim package ............... 18
1.5 A few words about this monograph..................... 21
2. The NECPA theory 27
2.1 Two-probe Hamiltonian................................ 27
2.2 NEGF formalism....................................... 30
2.3 Langreth theorem..................................... 32
2.4 NEGF in steady-state................................. 35
2.5 Dyson equation....................................... 39
2.6 Current formula...................................... 43
2.7 Surface Green’s function............................. 48
2.8 NECPA equations ..................................... 49
2.9 Current conservation and dephasing effect............ 56
2.10 A toy model.......................................... 61
3. The NECPA-LMTO method 67
3.1 Kohn-Sham equation.................................. 67
XVII
Atomistic Simulation of Quantum Transport
xviii
3.2 Muffin-tin orbital......................................... 69
3.3 Structure constant......................................... 72
3.4 Tail cancelation........................................... 73
3.5 Energy linearization ...................................... 74
3.6 LMTO Green’s function...................................... 76
3.7 Screening transform ....................................... 79
3.8 Physical quantities........................................ 81
3.9 Periodicity and Fourier transform.......................... 86
3.10 NECPA-LMTO formalism....................................... 88
3.11 Self-consistent calculation................................ 91
3.11.1 Flowchart.......................................... 91
3.11.2 Step-1 calculate structure constant.............. 93
3.11.3 Step-2 calculate self-energy....................... 94
3.11.4 Step-3 make an initial guess ..................... 95
3.11.5 Step-4 calculate atomic orbital................... 96
3.11.6 Step-5 calculate potential parameter............... 97
3.11.7 Step-6 solve the NECPA equations................... 98
3.11.8 Step-7 calculate energy moment.................... 100
3.11.9 Step-8 calculate charge density................... 100
3.11.10 Step-9 calculate charge and dipole................ 101
3.11.11 Step-10 calculate atomic potential with DFT . . . 102
3.11.12 Step-11 calculate Madelung potential.............. 103
3.11.13 Step-12 calculate total potential................. 103
3.12 Post-analysis calculation................................. 103
3.12.1 Density of states................................. 103
3.12.2 Transmission coefficient.......................... 104
3.12.3 Transmission variation ........................... 106
3.12.4 Band structure.................................... 107
3.12.5 CPA band structure................................ 107
3.13 Miscellaneous issues .................................... 108
3.13.1 Spin degree of freedom ........................... 109
3.13.2 Fermi level....................................... 109
3.13.3 Linearization center.............................. 110
3.13.4 Scalar relativistic equation...................... Ill
3.13.5 Wigner-Seitz radius............................... Ill
4. NanoDsim: the package design 113
4.1 Do you speak MATLAB? ..................................... 113
4.2 MATLAB: vectorization technique........................... 118
Contents xix
4.3 MATLAB: hybrid programming.............................. 120
4.4 MATLAB: object oriented programming..................... 125
4.5 NanoDsim: overall design.............................. 132
4.6 NanoDsim: dsim-solvers................................ 134
4.7 NanoDsim: dsim-calculators............................ 138
4.8 NanoDsim: dsim-classes............................... 139
4.9 NanoDsim: supporting libraries........................ 141
4.10 NanoDsim: implementation and debugging................ 143
5. NanoDsim: bulk systems 147
5.1 Bulk classes............................................ 148
5.1.1 @class_cpaBulk.................................. 148
5.1.2 @class_cpaAtom.................................. 150
5.1.3 @class_lmtoAtom ................................ 151
5.1.4 @class-lmtoOrbital.............................. 153
5.2 Bulk solver ............................................ 154
5.3 Structure constant...................................... 156
5.4 Ewald sum technique..................................... 159
5.5 Radial equation......................................... 165
5.6 Complex contour integral ............................... 171
5.7 CPA equations........................................... 176
5.8 Fermi level............................................. 181
5.9 Bulk calculator: band structure......................... 183
5.10 Bulk calculator: density of states...................... 185
6. NanoDsim: two-probe systems 189
6.1 Two-probe classes....................................... 189
6.1.1 @class_necpaTwoProbe............................ 190
6.1.2 @class_necpaAtom................................ 192
6.2 Two-probe solver........................................ 193
6.3 Ewald sum technique..................................... 195
6.3.1 2d Madelung potential .......................... 195
6.3.2 Surface Madelung potential...................... 200
6.3.3 Boundary condition............................. 204
6.4 Surface Green’s function................................ 206
6.4.1 Analytically solvable case...................... 206
6.4.2 Recursive method................................ 209
6.4.3 Eigenvalue method.............................. 212
xx Atomistic Simulation of Quantum Transport
6.4.4 A few comments.................................. 214
6.5 Real axis integral....................................... 216
6.6 k-integral in the Brillouin zone ....................... 219
6.6.1 Uniform k-sampling.............................. 220
6.6.2 Symmetric k-sampling............................ 221
6.6.3 Time-reversal symmetry........................... 226
6.7 NECPA equations ......................................... 232
6.8 Fermi level alignment.................................... 237
6.9 Two-probe calculator: transmission coefficient . .........239
6.10 Verification of the implementation ............. 241
7. NanoDsim: optimization and parallelization 247
7.1 Performance analysis..................................... 247
7.2 Memory issues ......................................... . 250
7.3 Speed issues............................................. 253
7.3.1 Order-N methods ................................. 253
7.3.2 Iterative methods................................ 254
7.3.3 Direct methods .................................. 257
7.3.4 Summary........................................ 260
7.4 Principal layer algorithm.................................261
7.4.1 Retarded Green’s function.........................261
7.4.2 Lesser Green’s function.......................... 265
7.4.3 Transmission coefficient........................ 266
7.4.4 Cost estimate ................................... 267
7.4.5 Implementation details........................... 269
7.5 MATLAB interface to MPI.................................. 269
7.6 Parallelization.......................................... 272
7.7 Benchmark ............................................. 274
7.8 Convergence issues....................................... 276
7.9 Error analysis............................................278
8. Kaleidoscope of the physics in disordered systems 283
8.1 Simple examples: bulk Cu, Fe, Co, Ni...............283
8.2 CPA vs supercell: Cu/Co alloy............................ 286
8.3 Si with uniaxial strain...................................288
8.4 Band offset of GaAs/AUGai-^As heterojunctions .... 292
8.5 NECPA vs supercell: Cu/Co interface...................... 294
8.6 Si transistors with localized doping..................... 298
Contents
xxi
8.7 Graphene transistors with disorder scattering..........302
8.8 Fe/MgO/Fe tunnel junctions ............................ 307
8.9 Cu films with surface scattering........................ 311
8.10 Concluding remarks .................................... 315
Appendix 319
A.l Atomic units .......................................... 319
A.2 Phase diagram of the toy model......................... 320
A.3 Classical transport vs quantum transport ..............324
A.3.1 Drift-Diffusion model.............................325
A.3.2 Effective-Mass model . .......................... 327
A.3.3 Numerical results ............................... 333
A.4 Lehmann spectrum of NEGF............................... 334
A.5 Low concentration approximation........................ 339
A.5.1 Multiple scattering theory .......................339
A.5.2 Transmission coefficient and transmission variation 342
A.6 Scattering states approach............................. 345
A.6.1 Bulk states...................................... 345
A.6.2 Wave scattering.................................. 347
A.6.3 Transmission coefficient......................... 350
A.6.4 Further discussion: group velocity................352
A.6.5 Further discussion: number of modes ............. 352
A.6.6 Further discussion: numerical issues..............353
A. 6.7 Summary.......................................... 355
A.7 Density matrix in clean bulk systems.................... 355
A.8 Connection to the CPA-NVC theory........................ 357
A.9 Explicit expressions of XC-functionals...................358
A.9.1 LDA: Perdew and Zunger (1981).................... 359
A.9.2 GGA: Perdew, Burke, and Ernzerhof (1996) . . . 360
A.9.3 MBJ: Tran and Blaha (2009)....................... 361
A.9.4 A few comments................................... 363
A. 10 Complex-valued and real-valued spherical harmonics . . . 363
A. 11 Gaunt coefficients...................................... 365
A, 12 Eigensolutions of TST and TSC matrices ................366
A. 13 Proof of the Wronskian identity........................ 368
A, 14 Numerical proof......................................... 369
A. 15 Transmission coefficient in the LMTO method..............370
A. 16 Specular scattering vs diffusive scattering..............373
A. 17 Fill the space with atomic spheres ......................376
XXII
Atomistic Simulation of Quantum Transport
A. 17.1 Regular structures.............................. 376
A. 17.2 Irregular structures............................ 378
A. 18 Symmetric k-sampling................................... 380
A. 19 Unfolding algorithm..................................... 385
A.20 Mixing algorithms ...................................... 386
A.21 Modified Fermi pole summation technique................. 389
A.22 Field effect transistor with gate terminals..............391
A.23 Algorithms for solving the Poisson equation..............393
A.23.1 Numerical discretization........................ 393
A.23.2 Algorithms in Id case........................... 395
A,23.3 Algorithms in 2d and 3d cases....................398
A.23.4 Nonorthogonal Poisson box....................... 399
A.23.5 Nonlinear Poisson equation.......................400
A.24 Locality in nonequilibrium............................. 402
A.25 Lanczos algorithm ..................................... 403
A.26 Preconditioner designed for quantum transport.......... 407
A.27 Content of the affiliated CD........................... 411
A.27.1 NanoDsim package................................ 411
A.27.2 ResearchCode package............................ 411
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| id | DE-604.BV043674616 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:32:10Z |
| institution | BVB |
| isbn | 9789813141421 9813141425 9789813141414 9813141417 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029087666 |
| oclc_num | 956323253 |
| open_access_boolean | |
| owner | DE-384 DE-703 |
| owner_facet | DE-384 DE-703 |
| physical | xxii, 413 Seiten Illustrationen, Diagramme CD-ROM (12 cm) |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Zhu, Yu Verfasser aut Atomistic simulation of quantum transport in nanoelectronic devices Yu Zhu and Lei Liu, NanoAcademic Technologies Inc., Canada New Jersey World Scientific [2016] xxii, 413 Seiten Illustrationen, Diagramme CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references "Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic device simulations. Nevertheless those packages are either black boxes (commercial codes) or accessible only to very limited users (private research codes). The purpose of this book is to open one of the commercial black boxes, and to demonstrate the complete procedure from theoretical derivation, to numerical implementation, all the way to device simulation. Meanwhile the affiliated source code constitutes an open platform for new researchers. This is the first book of its kind. We hope the book will make a modest contribution to the field of computational nanoelectronics"-- Nanoelectronics / Computer simulation Nanoelectromechanical systems Transport theory / Data processing Electron transport Quantum electronics / Mathematical models Datenverarbeitung Mathematisches Modell Computersimulation (DE-588)4148259-1 gnd rswk-swf Quantenphysik (DE-588)4266670-3 gnd rswk-swf Nanoelektronik (DE-588)4732034-5 gnd rswk-swf Nanoelektronik (DE-588)4732034-5 s Quantenphysik (DE-588)4266670-3 s Computersimulation (DE-588)4148259-1 s DE-604 Liu, Lei Sonstige oth Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029087666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhu, Yu Atomistic simulation of quantum transport in nanoelectronic devices Includes bibliographical references Nanoelectronics / Computer simulation Nanoelectromechanical systems Transport theory / Data processing Electron transport Quantum electronics / Mathematical models Datenverarbeitung Mathematisches Modell Computersimulation (DE-588)4148259-1 gnd Quantenphysik (DE-588)4266670-3 gnd Nanoelektronik (DE-588)4732034-5 gnd |
| subject_GND | (DE-588)4148259-1 (DE-588)4266670-3 (DE-588)4732034-5 |
| title | Atomistic simulation of quantum transport in nanoelectronic devices |
| title_auth | Atomistic simulation of quantum transport in nanoelectronic devices |
| title_exact_search | Atomistic simulation of quantum transport in nanoelectronic devices |
| title_full | Atomistic simulation of quantum transport in nanoelectronic devices Yu Zhu and Lei Liu, NanoAcademic Technologies Inc., Canada |
| title_fullStr | Atomistic simulation of quantum transport in nanoelectronic devices Yu Zhu and Lei Liu, NanoAcademic Technologies Inc., Canada |
| title_full_unstemmed | Atomistic simulation of quantum transport in nanoelectronic devices Yu Zhu and Lei Liu, NanoAcademic Technologies Inc., Canada |
| title_short | Atomistic simulation of quantum transport in nanoelectronic devices |
| title_sort | atomistic simulation of quantum transport in nanoelectronic devices |
| topic | Nanoelectronics / Computer simulation Nanoelectromechanical systems Transport theory / Data processing Electron transport Quantum electronics / Mathematical models Datenverarbeitung Mathematisches Modell Computersimulation (DE-588)4148259-1 gnd Quantenphysik (DE-588)4266670-3 gnd Nanoelektronik (DE-588)4732034-5 gnd |
| topic_facet | Nanoelectronics / Computer simulation Nanoelectromechanical systems Transport theory / Data processing Electron transport Quantum electronics / Mathematical models Datenverarbeitung Mathematisches Modell Computersimulation Quantenphysik Nanoelektronik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029087666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zhuyu atomisticsimulationofquantumtransportinnanoelectronicdevices AT liulei atomisticsimulationofquantumtransportinnanoelectronicdevices |